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Math Help - Need help on the steps to solving problem

  1. #1
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    Talking Need help on the steps to solving problem

    I have this problem:

    4/21=(3p-4)/7sqrt(p^2+20)

    I could use a detail step through process for solving this. I know that p=4 or -44/65
    I know that it comes downs to using the quadratic formula or factoring to solve the quadratic equation.

    my steps so far have been

    if 4/21=(3p-4)/7sqrt(p^2+20) then 4/21*7sqrt(p^2+20)=3p-4
    next I get 28sqrt(p^2+20)/21=3p-4
    then 4sqrt(p^2+20)/3=3p-4
    then I multiple both sides be the LCD (3) to eliminate the fraction
    I get 4sqrt(p^2+20)=9p-12)
    then I need help from here so I fully understand
    I know I need to square both sides and factor but I need to know all the steps
    thank you!
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  2. #2
    Super Member malaygoel's Avatar
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    since you have tried pretty well, here are the steps:

     4 \sqrt{p^2 + 20} = 9p-12

    squaring both sides

     16 (p^2 + 20)= {(9p-12)}^2

     16p^2 +320 = 81p^2 - 216 p +144

     16 p^2 - 81p^2 +216p +320-144=0

     -65p^2 +216p +176=0

     65p^2-216p-176=0

    can you take from here?
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  3. #3
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    I can take it from there is I use the quadratic formula :

    p=-b + or - sqrt b^2-4ac/2a

    could you though explain how to factor it properly?

    If I do (65p+22)(p-22) I don't get the answer but if I do (65p+44)(p-4) I do. but -8*22=-4*44
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  4. #4
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    Quote Originally Posted by colorado View Post
    I can take it from there is I use the quadratic formula :

    p=-b + or - sqrt b^2-4ac/2a

    could you though explain how to factor it properly?

    If I do (65p+22)(p-22) I don't get the answer but if I do (65p+44)(p-4) I do. but -8*22=-4*44
    It's p = \frac{-b-\sqrt{b^2 -4ac}}{2a} or p = \frac{-b+\sqrt{b^2 -4ac}}{2a}.
    Plugging in values for a, b and c, you'll get:
    p = 4 or p = -44/65
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  5. #5
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    thanks guys
    Last edited by colorado; January 6th 2011 at 11:15 AM.
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